In our model, each device trains a QNN of identical structure using \(n\)  bits of precision for quantization. We can express data more precisely if we increase \(n\)  at the cost of more energy usage. We can represent any given number in fixed-point format such as \([\Omega . \omega ]\) , where \(\Omega \)  is the integer part and \(\omega \)  is the fractional part of the given number [1]}. Here, we use one bit to represent the integer part and \((n-1)\)  bits for the fractional part. Then, the smallest positive number we can present would be \(\kappa = 2^{-n+1}\) , and the possible range of numbers with \(n\)  bits will be \([-1 ,1-2^{-n+1}]\) . Note that a QNN restricts the value of weights to [-1, 1]. We consider a stochastic quantization scheme [1]}, where any given \(w \in w\)  is quantized as follows:
\(Q(w) ={\left\lbrace \begin{array}{ll}\lfloor w \rfloor , & \quad \text{with probability} \quad \frac{\lfloor x \rfloor +\kappa - w}{\kappa },\\\lfloor w \rfloor + \kappa , & \quad \text{with probability} \quad \frac{w - \lfloor w \rfloor }{\kappa },\end{array}\right.}\) 
